Question: Simplify. Rewrite the expression in the form $4^n$. $\dfrac{4^{9}}{4^5}=$
$\begin{aligned} \dfrac{4^{9}}{4^5}&=4^{9-5} \\\\ &=4^4 \end{aligned}$ This follows from the general rule $\dfrac{x^m}{x^n}=x^{m-n}$. Note that the powers have the same base. We can also see this is correct by expanding the powers. $\begin{aligned} \dfrac{4^{9}}{4^5}&=\dfrac{\overbrace{\cancel 4\cdot \cancel 4\cdot \cancel 4\cdot \cancel 4\cdot \cancel 4\cdot 4\cdot 4\cdot 4\cdot 4}^\text{9 times}}{\underbrace{\cancel 4\cdot \cancel 4\cdot \cancel 4\cdot \cancel 4\cdot \cancel 4}_\text{5 times}} \\\\\\ &=\underbrace{4\cdot 4\cdot 4\cdot 4}_\text{4 times} \\\\ &=4^4 \end{aligned}$ In conclusion, $\dfrac{4^{9}}{4^5}=4^4$.